On Thu, Jun 28, 2018 at 11:26 AM, Bruno Marchal <marc...@ulb.ac.be> wrote:
*>You can store a sequence of numbers in one number. For example you can > store the sequence 7, 7, 7, 9, 8, 7, 9, 7, 6, 6 in the number x with > (unique) prime decomposition* > How can pure numbers do a unique prime decomposition? I don't want to know how you do it, I don't want to know how a computer does it, I want to know how a pure number does it. *> Then you can define, following Gödel [...]* > Definitions can't conjure things into existence. >* * > *You can define divides, =<, prime, etc. * > Definitions can't conjure things into existence. > > > *you would still need to define the exponentiation* > Definitions can't conjure things into existence. > > Matter is also unchanging and unchangeable in the Block-Universe picture. > Screw the Block-Universe picture, subjectively matter changes and subjectively pure numbers do not. >> >> How can the integer "7" be in a different state? > > > *>By adding one to it,* > The technical term for that is "8". The integer 8 has no memory , you can't say yesterday it was 7 so somebody must have added a 1 to it because yesterday 8 existed just as it does today and and tomorrow there will still be no change. I can store information in 7 magnetic spots on a computers hard drive but I can's store information in 7. > > > *Arithmetic indeed implements also the buggy computations, but that is a > relative notion. At the bare level of the sigma_1 truth, all computations > are correct, like a physical computer getting an incorrect answer due to > some bugs, does not violate the physical laws, nor the laws of arithmetic.* > If correct calculations exist in Plato's mystical heaven then incorrect ones must too, and for every correct calculation there are an infinite number of incorrect ones with no way of telling one from the other because in heaven nothing can actually *DO* anything. > > The physical reality and the arithmetical reality can contain buggy > computations, and correct one as well. > Arithmetical errors can happen in modern computers largely caused by cosmic rays but they are rare, but if you picked at computation at random from Plato's heaven the probability it is wrong is 100%. > >> >> >> And by "thing" I mean an object with the ability to exist in more than >> one state and yet still be recognizable. > > > > > Y*es, but such object does not need to be physical.* > Then if I add 1 to seven the number 7 no longer exists and neither does the number 1, and until I did that just now the number 8 did not exist. John K Clark > > > > > -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
